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Simplifying 7x2 + 34x + -39 = 0 Reorder the terms: -39 + 34x + 7x2 = 0 Solving -39 + 34x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.571428571 + 4.857142857x + x2 = 0 Move the constant term to the right: Add '5.571428571' to each side of the equation. -5.571428571 + 4.857142857x + 5.571428571 + x2 = 0 + 5.571428571 Reorder the terms: -5.571428571 + 5.571428571 + 4.857142857x + x2 = 0 + 5.571428571 Combine like terms: -5.571428571 + 5.571428571 = 0.000000000 0.000000000 + 4.857142857x + x2 = 0 + 5.571428571 4.857142857x + x2 = 0 + 5.571428571 Combine like terms: 0 + 5.571428571 = 5.571428571 4.857142857x + x2 = 5.571428571 The x term is 4.857142857x. Take half its coefficient (2.428571429). Square it (5.897959186) and add it to both sides. Add '5.897959186' to each side of the equation. 4.857142857x + 5.897959186 + x2 = 5.571428571 + 5.897959186 Reorder the terms: 5.897959186 + 4.857142857x + x2 = 5.571428571 + 5.897959186 Combine like terms: 5.571428571 + 5.897959186 = 11.469387757 5.897959186 + 4.857142857x + x2 = 11.469387757 Factor a perfect square on the left side: (x + 2.428571429)(x + 2.428571429) = 11.469387757 Calculate the square root of the right side: 3.386648455 Break this problem into two subproblems by setting (x + 2.428571429) equal to 3.386648455 and -3.386648455.Subproblem 1
x + 2.428571429 = 3.386648455 Simplifying x + 2.428571429 = 3.386648455 Reorder the terms: 2.428571429 + x = 3.386648455 Solving 2.428571429 + x = 3.386648455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.428571429' to each side of the equation. 2.428571429 + -2.428571429 + x = 3.386648455 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + x = 3.386648455 + -2.428571429 x = 3.386648455 + -2.428571429 Combine like terms: 3.386648455 + -2.428571429 = 0.958077026 x = 0.958077026 Simplifying x = 0.958077026Subproblem 2
x + 2.428571429 = -3.386648455 Simplifying x + 2.428571429 = -3.386648455 Reorder the terms: 2.428571429 + x = -3.386648455 Solving 2.428571429 + x = -3.386648455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.428571429' to each side of the equation. 2.428571429 + -2.428571429 + x = -3.386648455 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + x = -3.386648455 + -2.428571429 x = -3.386648455 + -2.428571429 Combine like terms: -3.386648455 + -2.428571429 = -5.815219884 x = -5.815219884 Simplifying x = -5.815219884Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.958077026, -5.815219884}
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